Though the Muscovy Trading Company was the initial spark that started London trading stocks, the idea grew over the next century, and by the end of the 17th century there were 140 joint stock companies. There was no stock exchange building then, and shares were traded at two coffee shops in central London: Garraway’s and Jonathan’s by a broker named John Castaing. It didn’t take long before traders figured out ways to rig markets and use insider information to their own benefit, so in 1697 brokers were required to be licensed and swear to act honorably in their stock trading.
Neither did it take long for the first stock “bubble" to form. In 1720, shares of the South Sea Company were offered, preceded by much hype and buzz from the company’s owner and the British government. Shares increased by nearly a factor of ten over the first six months of 1720, then rapidly plunged back to £124 each, which was even less than the initial starting price per share of £128.
When the coffee shop Jonathan’s burned down in 1748, brokers decided not to build a stock exchange building, but to build a new Jonathan’s and carry on trading there. Jonathan’s was, however, renamed “Stock Exchange," then finally the “Stock Subscription Room." It was officially designated as the London Stock Exchange in 1801.
After more intermediate moves, the London Stock Exchange ended up in 2004 at its current location at Paternoster Square near St. Paul’s Cathedral, but still within the official City of London.